A Common Scheduling Problem

A Common Scheduling Problem

One of my loyal readers has written in, asking me how I would solve a common scheduling problem. Here is the situation: a route that uses one bus is scheduled to operate every 60 minutes but, depending on the time of day, the route can take up to 70 minutes to complete. Of course, if a bus that is scheduled to operate every 60 minutes actually takes 70 minutes to complete then the bus will always be late and eventually end up missing a trip. There are four distinct ways we can fix this problem.

Overall, this problem demonstrates the difficulties schedulers have in scheduling routes that do not run very frequently. It is easy to assign blocks to buses on routes that operate frequent service, because there are a lot of trips to choose from. It is difficult to assign blocks to buses on routes that do not operate very often, because there are very few trips to choose from. In some cases the only alternatives may be to either attempt to squeeze the driver or to have the driver layover for a lengthy period of time.

This problem is likely to increase in the future as increased traffic congestion and ridership conspire to lower bus operating speed. Scheduling solutions that were elegant in their perfection in 1980, 1990, or 2000 may no longer work in 2011. Although routes that operate infrequently are often overlooked by agency staff because of their usual low ridership (sometimes they are called "loser lines"), perhaps the reason they have low ridership is that they suffer the scheduling problem referenced in this article. Application of these scheduling principles may operate like a bus route version of the hit reality show "The Biggest Loser".

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Add a Bus to the Route

Montreal Bus in Snow
A MCI Classic on a snowy but sunny winter day in Montreal. www.stm.info

The first thing we can do to fix this problem is to add a bus to the route. In the example discussed above, if one bus takes 70 minutes to complete a roundtrip then one bus can provide a 70-minute headway or two buses can provide a 35-minute headway. Although this is the easiest solution, it is the most expensive. If it costs $100 per hour to operate a bus and we add an additional bus on this route for eight hours per day, we are spending an additional $800 per day * 254 weekdays per year = $200,000 + per year to solve a scheduling problem. We are adding service not because of demand but because the route cannot be driven in its current configuration.

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Remove Bus Stops

A typical Boston bus stop showing the route numbers and destinations of buses stopping there. Many bus stops have schedule information attached below. Christopher MacKechnie

The second thing we can do to fix this problem is to remove bus stops. Removing bus stops is the only real way to increase bus operating speed ( refresh your memory on how we located bus stops ), as it is estimated that every bus stop where the bus actually stops adds 30 seconds to the running time of the bus. Routes that have average stop spacing of less than six hundred feet are good candidates for stop removal, although be aware that removing stops is sometimes politically perilous.

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Change the Route

One of the Charm City Circulator buses. The Charm City Circulator is a free service that covers all the sights in downtown Baltimore. Christopher MacKechnie

The second thing we can do is to change the route itself. Many circulator services who may fall into this scheduling problem operate meandering routes around a particular neighborhood (I am thinking of the Los Angeles DASH routes here). Straightening routes not only will lower the amount of time needed to complete them but will also likely increase ridership by more directly connecting destinations ( read my primer on how to design bus routes ).

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Interline the Route With Another Route

Another hybrid electric Orion waits to depart on its trip to York University from Downsview Station in Toronto, ON. By 2016, passengers will be able to take the subway directly to York University. Christopher MacKechnie

Of course, the above solution will not work with a route that already operates in a straight line connecting two destinations, and may not work in any case if the existing route is very productive passenger wise. In this case, the best solution is likely interlining. In interlining, we connect one bus route with another that shares a common terminus. Imagine two bus routes, both of which operate every 60 minutes; one takes 70 minutes to complete a roundtrip (assume layover is included) and one takes 50 minutes to complete a roundtrip. Separately, the one that takes 70 minutes will be constantly late and eventually miss a trip and the other one will have an excessive amount of layover. Together, they work perfectly. In order for interlining to work the two routes must share a common terminus, operate on the same headway, and one must need additional running time while the other has unnecessary layover time.


Overall, it is difficult to schedule buses when the desired headway does not fit with the running time. However, effective usage of one or more of the above four techniques will go a long way towards alleviating this problem.